Finite element methods for flow problems with moving boundaries and interfaces

This paper is an overview of the finite element methods developed by the Te am for Advanced Flow Simulation and Modeling (T*AFSM) [http://www.mems.rice .edu/TAFSM/] for computation flow problems with moving boundaries and inter faces. This class of problems include those with free surfaces, two-fluid i nterfaces, fluid-object and fluid-structure interactions, and moving mechan ical components. The methods developed can be classified into two main cate gories. The interface tracking methods are based on the Deforming-Spatial-D eforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, where the mesh moves to track the interface, with special attention paid to reduc ing the frequency of remeshing. The interface-capturing methods, typically used for free-surface and two-fluid flows, are based on the stabilized form ulation, over non-moving meshes, of both the flow equations and the advecti on equation governing the time-evolution of an interface function marking t he location of the interface. In this category, when it becomes necessary t o increase the accuracy in representing the interface beyond the accuracy p rovided by the existing mesh resolution around the interface,he Enhanced-Di scretization Interface-Capturing: Technique (EDICT) can be used to to accom plish that Real. In development of these two classes of methods, we had to keep in mind the requirement that tilt methods need to be applicable to 3D problems with complex geometries and that the associated large-scale comput ations need to be carried out on parallel computing platforms. Therefore ou r parallel implementations of these methods are based on unstructured grids and on both the distributed and shared memory parallel computing approache s. In addition to these two main classes of methods, a number of other idea s and methods have been developed to increase the scope and accuracy of the se two classes of methods. The review of all these methods in our presentat ion here is supplemented by a number numerical examples from parallel compu tation of complex, 3D flow problems.